Why am I not able to take neutral cities?

For example, I have 7 tanks, Player B has 3. Player B and I attack Houston's neutral 5 militias as my 1st move when I start my turn. Houston goes to Player B.

How do I take the city of Houston for myself?

Are you ally/peace with him? Did he have more different type of unit? Then yes he will get it

Peace with other player. Is there a priority order for taking cities?

No, its random if you both are allied/peace except its your home country (if someone took it and left)